States have existed far longer. "Nation state" refers specifically to a state which coincides with a cultural or ethnic group. If you had to choose a starting point for the idea of the nation state, the Treaty of Westphalia is one of the more reasonable.

Again, it depends on your definition of "state." If you're using the term interchangeably with the much broader term "government," which can include even the smallest and most primitive family or tribe power structures, then you can probably consider the state to be older than marriage (I actually think there's still room for debate even then, depending also on the definition of "marriage").